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On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces

Author

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  • Farrukh Mukhamedov
  • Mansoor Saburov

Abstract

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I‐nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptotically I‐nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed‐convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.

Suggested Citation

  • Farrukh Mukhamedov & Mansoor Saburov, 2012. "On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:281383
    DOI: 10.1155/2012/281383
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    References listed on IDEAS

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    1. C. E. Chidume & E. U. Ofoedu, 2009. "A New Iteration Process for Approximation of Common Fixed Points for Finite Families of Total Asymptotically Nonexpansive Mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-17, December.
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    Cited by:

    1. Bin-Chao Deng & Tong Chen & Yi-Lin Yin, 2014. "Strong Convergence Theorems for Mixed Equilibrium Problem and Asymptotically I‐Nonexpansive Mapping in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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